On the Navier-Stokes “Millenium Prize”

There has been some (predictably confused) press recently about the publication of a proposed solution to one of the “Millenium Prize” mathematical problems set by the Clay Mathematics Institute.

The problem, which is defined with admirable clarity here (PDF), is about the nature of the solutions to the Navier-Stokes equations, which are the nonlinear partial differential equations at the heart of most investigations into fluid flow, at least for Newtonian fluids. Passing over the mathematical technicalities, the challenge is this: given arbitrary but reasonable initial conditions, prove that the equations have smooth solutions valid for all time, or that they don’t. Periodic solutions are allowed.

The sudden excitement in the press is due to the claim by a professor in Kazakhstan to have solved this problem. Why would reporters get worked up over mathematics? They wouldn’t, of course; but the prize is for a million dollars. There are seven problems, set in the year 2000, and one has been solved, by a man who refused the prize with disdain.

The proposed solution exists in the form of a paper in Russian (PDF), with a brief summary in English, that has not yet appeared in a peer reviewed journal. There is a public, ongoing effort to translate it in to English. If you are qualified to assist in the translation, they are looking for help.